The Predators blew a two-goal lead in the final 2:07 of regulation but still managed to win their fourth straight game. They completed a sweep of the New York-metropolitan area teams this week.
Paul Kariya set up first-period power-play goals by Jason Arnott and Erat and Scott Nichol scored short-handed in the second for Nashville, which had eight shots on goals over the final two periods and the overtime.
Brian Gionta scored twice, including the tying goal with 11.6 seconds to go in regulation. Scott Gomez had the other goal for the Devils.
Mason finished with 30 saves filling in for Tomas Vokoun. He also stopped Zach Parise, Gionta and Patrik Elias in the shootout.
Erat scored on the Predators' third attempt, snapping a shot over the glove of Scott Clemmensen, who had 15 saves in his first start of the year.
The Devils, who rallied from a three-goal third-period deficit at home earlier this season to beat Toronto 7-6 in a shootout, staged another comeback against the Predators, who beat the Islanders on Monday and the Rangers on Wednesday.
Gomez started it by lifting the rebound of a Gionta shot over Mason's shoulder.
Gionta, who scored all three third-period goals in the win over Toronto, scored his sixth of the season and second of the game from the right faceoff circle with 11.6 seconds to play in regulation.
Kariya's assists were sandwiched around Gionta's first goal.
Arnott was the first beneficiary of Kariya's passing, converting from right in front at 2:10 on the first shot that Clemmensen faced this season.
Mason also was beaten on the Devils' first shot, a power-play goal by Gionta after nice passes by Gomez and Elias.
Erat gave the Predators a 2-1 lead after taking a Kariya pass and scoring from between the circles on a shot that seemed to hit off Devils defenceman Paul Martin.
Nichol deflected a shot by defenceman Ryan Suter after beating Gomez on a faceoff.
Notes: Devils rookie C Travis Zajac missed the third period because of soreness. ... RW Steve Sullivan, who was leading the Predators with seven points, sat out with back spasms. ... The Devils scored on their first power play, ending a streak of 11 straight kills by the Predators. ... Kimmo Timonen had an assist in his 500th game with Nashville. ... This was the only regular-season game between the teams this season.